OK, you get to take additional actions, that's like having a Leo De Luca in play for a few turns with some restrictions. But actually, since you get to take that additional action during any player window, not just on your own turn, you can do some more unusual things even outside of the investigation phase. There may be some shenanigans you can pull during the Mythos phase or the Upkeep phase, but the most likely target is in the player window in the Enemy phase after Hunter enemies move and engage but before any enemy attacks. You can do a basic fight to finish off a 1 HP enemy, or evade one to prevent it from dealing you any damage or horror. Or -- since playing an event is a basic action, as long as it doesn't have a Bold action modifier on it -- you can play an event card. If you don't mind or can avoid the AoO, or if the enemy isn't going to be engaging you, then you have some great options, like Call for Backup, Sneak Attack (2), and Small Favor. Coup de Grâce, Dynamite Blast (2), Blood-Rite, Manipulate Destiny, Gaze of Ouraxsh don't provoke an AoO, and may be used for different situations.
How about using that during your basic action? Most full-time Mystics will likely use this additional action for an evasion in a pinch, since they likely have a spell or two to do damage or investigate and get additional benefits. A basic evade is probably the most common way investigators with high evade anyhow, so it's not surprising this would be most likely choice for Close the Circle. But "activate" is also a basic action, so you can use this on tests on scenario cards that are otherwise difficult. Yes, most treachery cards have tests on them already, like Dreams of R'lyeh, but Locked Door is common enough. A few of the more recent campaigns have a good chunk of treachery cards at your location or in your threat area that don't give you a option, so be on the lookout if you're trying to leverage your Close the Circle.
